Using Automatic Differentiation as a General Framework for Ptychographic Reconstruction

Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed, and those calculated from a present guess of the object. Efficient minimization methods require analytical calculation of the derivatives of the error metric, which is not always straightforward. This limits our ability to explore variations of basic imaging approaches. In this paper, we propose to substitute analytical derivative expressions with the automatic differentiation method, whereby we can achieve object reconstruction by specifying only the physics-based experimental forward model. We demonstrate the generality of the proposed method through straightforward object reconstruction for a variety of complex ptychographic experimental models.Comment: 23 pages (including references and supplemental material), 19 externally generated figure file

A differentiable forward model for the concurrent, multi-peak Bragg coherent x-ray diffraction imaging problem

We present a general analytic approach to spatially resolve the nano-scale lattice distortion field of strained and defected compact crystals with Bragg coherent x-ray diffraction imaging (BCDI). Our approach relies on fitting a differentiable forward model simultaneously to multiple BCDI datasets corresponding to independent Bragg reflections from the same single crystal. It is designed to be faithful to heterogeneities that potentially manifest as phase discontinuities in the coherently diffracted wave, such as lattice dislocations in an imperfect crystal. We retain fidelity to such small features in the reconstruction process through a Fourier transform -based resampling algorithm designed to largely avoid the point spread tendencies of commonly employed interpolation methods. The reconstruction model defined in this manner brings BCDI reconstruction into the scope of explicit optimization driven by automatic differentiation. With results from simulations and experimental diffraction data, we demonstrate significant improvement in the final image quality compared to conventional phase retrieval, enabled by explicitly coupling multiple BCDI datasets into the reconstruction loss function.Comment: 30 pages, 23 figure

Genome-wide expression profiling and functional characterization of SCA28 lymphoblastoid cell lines reveal impairment in cell growth and activation of apoptotic pathways

BACKGROUND: SCA28 is an autosomal dominant ataxia associated with AFG3L2 gene mutations. We performed a whole genome expression profiling using lymphoblastoid cell lines (LCLs) from four SCA28 patients and six unrelated healthy controls matched for sex and age. METHODS: Gene expression was evaluated with the Affymetrix GeneChip Human Genome U133A 2.0 Arrays and data were validated by real-time PCR. RESULTS: We found 66 genes whose expression was statistically different in SCA28 LCLs, 35 of which were up-regulated and 31 down-regulated. The differentially expressed genes were clustered in five functional categories: (1) regulation of cell proliferation; (2) regulation of programmed cell death; (3) response to oxidative stress; (4) cell adhesion, and (5) chemical homeostasis. To validate these data, we performed functional experiments that proved an impaired SCA28 LCLs growth compared to controls (p\u2009<\u20090.005), an increased number of cells in the G0/G1 phase (p\u2009<\u20090.001), and an increased mortality because of apoptosis (p\u2009<\u20090.05). We also showed that respiratory chain activity and reactive oxygen species levels was not altered, although lipid peroxidation in SCA28 LCLs was increased in basal conditions (p\u2009<\u20090.05). We did not detect mitochondrial DNA large deletions. An increase of TFAM, a crucial protein for mtDNA maintenance, and of DRP1, a key regulator of mitochondrial dynamic mechanism, suggested an alteration of fission/fusion pathways. CONCLUSIONS: Whole genome expression profiling, performed on SCA28 LCLs, allowed us to identify five altered functional categories that characterize the SCA28 LCLs phenotype, the first reported in human cells to our knowledge. \ua9 2013 Mancini et al.; licensee BioMed Central Ltd

Ptychography

Ptychography is a computational imaging technique. A detector records an extensive data set consisting of many inference patterns obtained as an object is displaced to various positions relative to an illumination field. A computer algorithm of some type is then used to invert these data into an image. It has three key advantages: it does not depend upon a good-quality lens, or indeed on using any lens at all; it can obtain the image wave in phase as well as in intensity; and it can self-calibrate in the sense that errors that arise in the experimental set up can be accounted for and their effects removed. Its transfer function is in theory perfect, with resolution being wavelength limited. Although the main concepts of ptychography were developed many years ago, it has only recently (over the last 10 years) become widely adopted. This chapter surveys visible light, x-ray, electron, and EUV ptychography as applied to microscopic imaging. It describes the principal experimental arrangements used at these various wavelengths. It reviews the most common inversion algorithms that are nowadays employed, giving examples of meta code to implement these. It describes, for those new to the field, how to avoid the most common pitfalls in obtaining good quality reconstructions. It also discusses more advanced techniques such as modal decomposition and strategies to cope with three-dimensional () multiple scattering